Question

For a given integer n>1, the smallest integer d>1 that divides n is a prime factor. We can find the prime factorization of n if we find d and then replace n by the quotient of n divided by d, repeating this until n becomes 1 . Write a java program that uses a stack to print the prime factors of a positive integer in descending order. For example, for n=3960, your program should produce

Answer 1

The question involves writing a Java program that computes the prime factors of a given integer using a stack and prints them in descending order. A loop is used to find and push prime factors onto the stack until the integer is reduced to 1. Finally, the stack is popped to print the factors.

Step-by-step explanation:

The question is about using a Java program to find and print the prime factors of a given positive integer n in descending order, using a stack data structure. The process involves repeatedly finding the smallest integer d greater than 1 that divides n and is a prime factor. This prime factor is pushed to the stack and n is replaced by the quotient of n divided by d. This step is repeated until n becomes 1. Finally, the stack is popped to print the prime factors in descending order, as required by the problem statement.

The essential parts of the Java program would be:

• A method to find the smallest prime factor d of a number.
• A loop that performs the division and pushes the prime factors onto the stack.
• A loop to pop and print elements from the stack in descending order.

Here's a simplified structure of the Java program:

import java.util.Stack;

public class PrimeFactors {
public static void main(String[] args) {
int n = 3960;
Stack<Integer> stack = new Stack<>();

for (int d = 2; n > 1; d++) {
while (n % d == 0) {
stack.push(d);
n /= d;
}
}

while (!stack.isEmpty()) {
System.out.print(stack.pop() + " ");
}
}

// Additional methods could be added here if necessary.
}